Laser trimming to tune the resonance frequency of a spiral resonator, the characteristics of a high temperature superconductor filter comprised of spiral resonators, or the resonance frequency of a planar coil

ABSTRACT

This invention provides a laser trimming method for tuning the frequency of a spiral resonator, and for improving the characteristics of a high temperature superconductor filter comprised of high temperature superconductor spiral resonators, by tuning the individual high temperature superconductor spiral resonators. This invention also provides a method for tuning the resonance frequency of a high temperature superconductor planar coil. This invention also provides a laser ablation process for creating high temperature superconductor circuit elements.

This application claims the benefit of U.S. Provisional Application No.60/523,988, filed on Nov. 21, 2003, which is incorporated in itsentirety as a part hereof for all purposes.

FIELD OF THE INVENTION

This invention relates to laser trimming to tune the resonance frequencyof a spiral resonator, to tune individual spiral resonators of a hightemperature superconductor filter to improve the filter characteristics,or to tune the resonance frequency of a planar coil.

BACKGROUND OF THE INVENTION

High temperature superconductor (HTS) filters have applications intelecommunication, instrumentation and military equipment. The HTSfilters have the advantages of extremely low in-band insertion loss,high out-of-band rejection and steep skirts due to the extremely lowloss in the HTS materials. In a typical design, HTS filters andmini-multiplexers are comprised of spiral resonators.

Filter performance is highly dependent on the frequencies of theresonators of which the filter was comprised. In turn, variations incircuit parameters such as resonator patterning, substrate thickness anddielectric constant, and HTS material properties affect the frequency ofthe resonators. It is both difficult and costly to try to control theseparameters precisely during production. The difficulty in producing thedesired HTS filter pattern increases as the number of resonators orpoles in the filter increases.

It is therefore desirable to tune the filters after they have beenproduced. One approach to tuning the center frequency of such a filterproposed by Shen, WO 01/41251, involves providing a plate spaced adistance apart from and opposite to the HTS filter. The plate contains aconductive film, preferably a HTS film, on at least a portion of thesurface of the plate that faces the filter. The distance between theplate and the filter can be adjusted to tune the center frequency of thefilter. Alternatively, the individual resonators of the filter can bemechanically tuned by adjusting a screw or a dielectric rod. However,since the resonators generally vary in a random fashion, each pole ofthe filter must be individually tuned and the tuning of each poleaffects every other pole in the filter. The tuning process can typicallytake hours to perform.

Humphreys, U.S. Ser. No. 03/048,148, and N. J. Parker et al, 2000 IEEEMTT-S, page 1971, disclose tuning a microwave or RF circuit by directinga laser beam onto the microwave or RF circuit so as to alter thematerial properties of selected areas of the microwave or RF circuit.Results are disclosed for a simple microstrip λ/2 resonator and apseudo-elliptic filter comprised of 3 simple microstrip λ/2 resonators.They disclose that it is easier to increase the resonator frequenciesthan to reduce them.

An object of the present invention is to tune the resonance frequency ofa HTS spiral resonator or a HTS coil and to improve the production yieldof HTS filters comprised of HTS spiral resonators by providing a methodfor tuning the characteristics of such a filter by tuning individual HTSspiral resonators.

SUMMARY OF THE INVENTION

This invention provides a method for tuning the resonance frequency of ahigh temperature superconductor spiral resonator by ablating portions ofthe high temperature superconductor spiral resonator with a laser beam.

The resonance frequency of a high temperature superconductor spiralresonator can be increased by ablating the high temperaturesuperconductor at the outer end of the high temperature superconductorspiral of the spiral resonator. The resonance frequency of a hightemperature superconductor spiral resonator can be decreased by ablatingthe high temperature superconductor at the inner end of the hightemperature superconductor spiral of the spiral resonator. Lasertrimming at interior locations along the high temperature superconductorspiral resonator results in increases or decreases in the resonancefrequency depending upon the location of the trimming. Increases in theresonance frequency result when trimming at interior locations at whichthe current density is sufficiently low, and decreases in the resonancefrequency result when trimming at interior locations where the currentdensity is sufficiently high. The resulting resonance frequency shiftsfrom multiple trimmings are additive.

This invention also provides a method for tuning the filtercharacteristics of a high temperature superconductor filter comprised ofat least two high temperature superconductor spiral resonators byablating portions of one or more of the high temperature superconductorspiral resonators with a laser beam.

This invention also provides a method for tuning the resonance frequencyof a high temperature superconductor planar coil by ablating portions ofthe high temperature superconductor planar coil with a laser beam.

The resonance frequency of a high temperature superconductor planar coilcan be increased by ablating the high temperature superconductor at theouter end of the high temperature superconductor of the planar coil orat the inner end of the high temperature superconductor of the planarcoil. Laser trimming at interior locations along the high temperaturesuperconductor planar coil results in increases or decreases in theresonance frequency depending upon the location of the trimming.Increases in the resonance frequency result when trimming at interiorlocations at which the current density is sufficiently low, anddecreases in the resonance frequency result when trimming at interiorlocations where the current density is sufficiently high. The resultingresonance frequency shifts from multiple trimmings are additive.

This invention also provides a process for forming a high temperaturesuperconductor circuit element, comprising:

-   -   a) forming a film of a high temperature superconductor material        on a substrate; and    -   b) ablating selected regions of the high temperature        superconductor film with a laser beam while protecting from        ablation other regions of the high temperature superconductor        film that form a pattern of the circuit element.

The circuit element can be a spiral resonator, a filter, a coil or anyother useful high temperature superconductor component.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an 8-pole filter comprised of eight HTS rectangular spiralresonators and seven HTS inter-resonator couplers.

FIG. 2 shows a rectangular spiral resonator with some trimming locationsidentified.

FIG. 3 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 1before the laser trimming of the invention.

FIG. 4 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 1 afterthe laser trimming of the invention.

FIG. 5 shows the rectangular spiral resonator used in Examples 2-4 andthe locations of the material removed.

FIG. 6 shows the resonance curves and frequencies for Examples 2-4.

FIGS. 7A and 7B show the rectangular spiral resonator used in Examples5-7 and the locations of the material removed.

FIG. 8 shows the resonance curves and frequencies for Examples 5-7.

FIGS. 9A and 9B show the rectangular spiral resonator used in Examples8-16 and the locations of the material removed.

FIG. 10 shows the rectangular spiral resonator used in Examples 17-27and identifies various locations on the rectangular spiral resonator.

FIG. 11 shows an enlarged view of the outer end a of the rectangularspiral resonator shown in FIG. 10 and the locations of material removedin Examples 17-20.

FIG. 12 shows an enlarged view of the inner end n of the rectangularspiral resonator shown in FIG. 10 and the locations of material removedin Examples 21-24.

FIG. 13 shows the rectangular spiral resonator of FIG. 10 with typicallocations of material removed in Examples 25-27.

FIG. 14 shows plots of the shift in resonance frequency and the peakcurrent density for each of the near corner locations where material wasremoved in Example 25.

FIG. 15 shows plots of the shift in resonance frequency and the peakcurrent density for each of the inner edge elocations where material wasremoved in Example 26.

FIG. 16 shows plots of the shift in resonance frequency and the peakcurrent density for each of the outer edge locations where material wasremoved in Example 27.

FIG. 17 is a plot of the frequency shifts observed in Examples 25, 26and 27 versus the peak current density at the location where materialwas removed.

FIG. 18 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 28before the laser trimming of the invention.

FIG. 19 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 28after the laser trimming of the invention.

FIG. 20 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 29before the laser trimming of the invention.

FIG. 21 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 29after the laser trimming of the invention.

FIG. 22 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 30before the laser trimming of the invention.

FIG. 23 shows the S₂₁ and the S₁₁ of the 8-pole filter of Example 30after the laser trimming of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides a method for tuning the resonancefrequency of a high temperature superconductor spiral resonator by lasertrimming the high temperature superconductor spiral resonator. Thismethod provides for readily increasing or decreasing the resonancefrequency of the high temperature superconductor spiral resonator. Thepresent invention also provides a method for tuning the characteristics,such as the filter characteristics, of a high temperature superconductorfilter comprised of at least two high temperature superconductor spiralresonators by laser trimming one or more of the high temperaturesuperconductor spiral resonators. This method makes it possible toincrease or decrease the center frequency of the HTS filter as well asto hold the center frequency essentially constant while adjusting theresponse within the band-pass region, or to both change the centerfrequency of the HTS filter and adjusting the response within theband-pass region. When the HTS filter is further comprised of HTSinter-resonator couplers, laser trimming the HTS inter-resonatorcouplers decreases the bandwidth of the band-pass region. Lasertrimming, or trimming, is the use of a laser beam to ablate hightemperature superconductor material.

Typically, an HTS spiral resonator, or filter comprised of spiralresonators, is prepared by depositing a film of HTS material on anappropriate single crystal substrate and then coating the HTS materialwith photoresist. A mask with the spiral resonator or filter pattern isthen placed on the photoresist and exposed to actinic light. Thephotoresist is developed, and the portion of the HTS material exposedwhen the resist is developed is removed, e.g. by argon ion etching. Theremaining resist is then removed, e.g. by oxygen etching. Otherpreparations of the HTS spiral resonator or filter can also be used. Nomatter how the HTS spiral resonator or filter is prepared, the lasertrimming method of this invention can subsequently tune the HTS spiralresonator or filter.

A novel one-step process for creating the HTS filter from the HTS filmis to laser etch the HTS film to form and tune the filter. Thistechnique can also be used to create HTS resonators, HTS coils and otherHTS circuit elements. Preferably, the HTS coils are planar coils, i.e.surface coils. A laser can be programmed to direct the laser beam toimpact those regions of the HTS film that are to be ablated by the laserbeam and to avoid those regions of the HTS film that form the desiredpattern of the HTS element.

An 8-pole or 8-resonator HTS filter comprised of 8 rectangular HTSspiral resonators and 7 HTS inter-resonator couplers is shown in FIG. 1.An HTS filter of this design was used in Example 1 and is furtherdescribed there. FIG. 2 shows one of the HTS spiral resonators. Thisspiral resonator comprises a high temperature superconductor line ofwidth w oriented in a rectangular spiral fashion such that adjacentlines of the spiral resonator are spaced from each other by a gapdistance d and so as to provide a central opening 1 within the spiralresonator.

The resonance frequency is

f _(s)=1/{2π[LC] ^(1/2)}

wherein L and C are the inductance and capacitance of the spiralresonator. Equivalently, resonance occurs when the length of the spiralresonator equals nλ/2, where λ is the wavelength of the propagatingelectromagnetic wave and n is an integer. The HTS spiral resonators canhave different shapes, including rectangular, rectangular with roundedcorners, polygonal with more than four sides and circular. Preferably,all the HTS spiral resonators in a filter have the same shape. Aconductive tuning pad may be placed in the central opening 1 tofine-tune the frequency of the spiral resonator. This tuning pad can bea high temperature superconductor and can be ablated during the lasertrimming process to adjust the resonance frequency.

It has now been found that the resonance frequency of a HTS spiralresonator can be readily increased or decreased by trimming the HTSspiral line at particular locations. For example, trimming, i.e.ablating, high temperature superconductor material at the outer end ofthe HTS spiral, e.g. at location 2 shown in FIG. 2, increases theresonance frequency. In contrast, trimming high temperaturesuperconductor material at the inner end of the HTS spiral, e.g. atlocation 3 in FIG. 2, decreases the resonance frequency.

The resonance frequency can also be readily increased or decreased bytrimming at interior locations along the HTS spiral. Interior locationsare any locations along the HTS spiral between the outer end 2 and theinner end 3, e.g. at locations 4 to 8 on FIG. 2. Whether there is anincrease or decrease in the resonance frequency when trimming atinterior locations, and (if so) the magnitude of the frequency change,depends on the location along the HTS spiral where trimming occurs; and,for a given distance along the HTS spiral, also depends on whether thelocation is on the outer edge of the HTS spiral line (e.g. location 7)or on the inner edge of the HTS spiral line (e.g. locations 3, 4, 5 and8).

This dependence of the change in resonance frequency on trimminglocation is a result of the fact that different locations have differentcurrent densities. There is a variation in current density at differentlocations along the HTS spiral line, and between the outer edge andinner edge of the HTS line. For a given amount of material trimmed,there is a linear relation between the current density at the trimminglocation and the change in frequency. Trimming at interior locations atwhich the current density is low results in resonance frequencyincreases. At trimming locations with somewhat larger current densities,the magnitude of the increase in resonance frequency becomes smaller forthe same amount of trimming. At trimming locations where the currentdensity is high, trimming results in a decrease in the resonancefrequency. The larger the current density at a location, the larger thedecrease in the resonance frequency obtained from a particular amount oftrimming.

A location, such as an interior location, at which the current densityis sufficiently low such that the resonance frequency is increased whenthe HTS spiral line is trimmed at that location will generally have acurrent density that is less than about 25% of the maximum currentdensity observed along the HTS spiral line. A location, such as aninterior location, at which the current density is sufficiently highsuch that the resonance frequency is decreased when the HTS spiral lineis trimmed at that location will generally have a current density thatis greater than about 25% of the maximum current density observed alongthe HTS spiral line. The amount of current density that will produce anincrease or decrease in resonance frequency is not, however, invariablylimited to those ranges.

For example, trimming locations 4 to 6 are far enough along the HTSspiral line from the outer end, and are on the inner edge of the HTSspiral line, such that the current densities are sufficiently high atthose locations to result in resonance frequency decreases when trimmed.As indicated above, for a given amount of trimming the decrease in theresonance frequency is most effective in regions of highest currentdensity. Larger decreases in resonance frequency occur for lasertrimming at location 4, which is closer to a spiral resonator cornerwhere a higher current density is expected and observed, compared tothat found for the same amount of laser trimming at location 5, which isfarther from the corner and has a smaller current density. Location 6,which is farthest from the corner, has the lowest current density ofthese three locations, and therefore shows the smallest shift inresonance frequency when trimmed.

The magnitude of the increase or decrease in the resonance frequencydepends on the amount of HTS ablated. Choice of various differentinterior locations provides a different sensitivity, i.e. a differentmagnitude of increase or decrease in frequency, for the same amount ofablation, depending on the current density at the location.

The characteristics of an HTS filter comprised of at least two HTSspiral resonators can be changed in various ways by laser trimming. Ifthe center frequency of the band-pass is the desired frequency, thein-band characteristics can be improved by laser trimming one or more ofthe individual HTS spiral resonators so that all of the HTS spiralresonators have a resonance frequency equal to the band-pass centerfrequency. If the center frequency of the band-pass is not the desiredfrequency, a lower or higher center frequency can be obtained by lasertrimming the individual HTS spiral resonators so that all of the HTSspiral resonators have a resonance frequency equal to the lower orhigher center frequency. In addition, the in-band characteristics willbe improved.

The inter-resonator couplings between adjacent HTS spiral resonators inthe HTS filter are provided by the overlapping of the electromagneticfields at the edges of the adjacent spiral resonators. In addition, asshown in FIG. 1, HTS lines can be provided between the HTS spiralresonators to serve as inter-resonator couplers. When HTSinter-resonator couplers are provided, these couplers can be lasertrimmed to decrease the bandwidth of the band-pass region.

The method for tuning the resonance frequency of a high temperaturesuperconductor planar coil is analogous to that used for tuning theresonance frequency of a spiral resonator with one exception. Trimminghigh temperature superconductor material at the outer end of the HTSplanar coil increases the resonance frequency. The resonance frequencycan be readily increased or decreased by trimming at interior locationsalong the HTS planar coil. Increases in the resonance frequency resultwhen trimming at interior locations at which the current density issufficiently low, and decreases in the resonance frequency result whentrimming at interior locations where the current density is sufficientlyhigh.

The one exception to analogous behavior of the HTS planar coil trimmingand HTS spiral resonator trimming involves the trimming of hightemperature superconductor material at the inner end of the HTS planarcoil. Since the coupling at the inner end of a planar coil is not nearlyas strong as the coupling at the inner end of a spiral resonator,trimming high temperature superconductor material at the inner end ofthe HTS planar coil results in an increase in resonance frequencyinstead of the decrease in resonance frequency found when trimming atthe inner end of a spiral resonator. The resulting resonance frequencyshifts from multiple trimmings are additive.

In all of the embodiments described above, it is preferred that the hightemperature superconductor is selected from the group consisting ofYBa₂Cu₃O₇, Tl₂Ba₂CaCu₂O₈, TlBa₂Ca₂Cu₃O₉, (TlPb)Sr₂CaCu₂O₇ and(TlPb)Sr₂Ca₂Cu₃O₉. A single crystal substrate is independently selectedfrom the group consisting of LaAlO₃, MgO, LiNbO₃, sapphire (Al₂O₃) andquartz. LaAlO₃ and sapphire are preferred. The presence of a buffer orintermediate layer of an oxide on the substrate before the deposition ofthe superconductor can be useful in promoting growth of thesuperconductor film. Reference herein to “depositing a film of HTSmaterial on an appropriate single crystal substrate” will thus includedirect intimate contact with the substrate as well as intimate contactwith an intermediate or buffer layer on the substrate.

The laser trimming method for tuning HTS resonators, HTS filters and HTScoils and for forming HTS circuit elements can be carried out withvarious lasers, but an excimer laser is preferred. It is important to beable to carry out the laser trimming while the HTS circuit element is atliquid nitrogen temperature so that the HTS material is superconductiveand changes in the HTS circuit element performance can be monitoredduring the trimming process. Provisions must be made for electricalconnections between the HTS circuit element and a circuit analyzer.

The advantageous effects of this invention are demonstrated by a seriesof examples, as described below. The embodiments of the invention onwhich the examples are based are illustrative only, and do not limit thescope of the appended claims.

In Examples 1, 28, 29 and 30 that follow, the following apparatus andprocedure are used. A 193 nm excimer laser (Lambda Physik LPX.^(□) 220,Gottingen, Germany) equipped with 0.1 μm precision X, Y, Z, theta stageand with in process and targeting cameras is used for the trimming. Arectangular variable aperture or image projection mask is used toconfigure the laser demagnification to a 50 μm×50 μm square spot. Thelaser voltages and variable transmission ranges are configured to yieldbetween 500 and 1200 mJ/cm². Preferred is a 12× demagnification toprovide the 50 μm×50 μm focussed square spot with a yield of between 750and 1000 mJ/cm². The substrate with the filter is mounted onto a copperfilter mount. A liquid nitrogen fixture provides a reservoir for liquidnitrogen and enables electrical connections between the filter and theanalyzer, an Agilent 8753 Vector Network Analyzer (Agilent Technologies,Palo Alto, Calif.). This allows the filter to be laser trimmed at liquidnitrogen temperatures while simultaneously powering and monitoringfilter response to the trimming.

The network analyzer provides the plots of S₁₁ and S₂₁. S₁₁ is themagnitude of the reflection coefficient from the input port. S₂₁ is themagnitude of the transmitting coefficient from the input port to theoutput port. S₁₁ and S₂₁ are important parameters for practicalapplications of a filter and are used here to characterize the changesin the filter as a result of the laser trimming. Outside the band-passregion, S₁₁ should be nearly 1, i.e. about 0 dB. The magnitude of S₁₁ inthe band-pass region should be as low as possible. S₂₁ should be nearly1, i.e. about 0 dB in the band-pass region. The magnitude of S₂₁ outsidethe band-pass region should be as low as possible.

The copper filter mount with the mounted substrate is secured onto theliquid nitrogen fixture. The liquid nitrogen fixture is mounted onto theX, Y, Z, theta stage of the laser. The filter surface must be planarwith the focal point of the laser. Laser test bursts are taken onto anon-critical area of the filter surface to ensure that the laser is infocus and both cameras are aligned. An aluminum cover is placed over thefilter and secured onto the copper filter mount. The aluminum cover hasan opening that extends over the entire surface of the aluminum cover.The aluminum cover provides a support for a quartz window that issecured to the aluminum cover with tape. The quartz window containsliquid nitrogen boil-off over the filter, and prevents condensationand/or frost from forming on the filter surface while allowing the 193nm UV radiation to transmit through for trimming. A temporary liquidnitrogen fixture cover is placed over the liquid nitrogen fixture,aluminum cover and quartz window to prevent condensation accumulation onthe quartz window surface.

Dry nitrogen gas is used to purge the laser beam delivery optics, thebeam delivery nozzle and the liquid nitrogen fixture. This purge iscontinued for 15-20 minutes. RF cables are then connected to the inputand output of the filter and to the network analyzer. Liquid nitrogen isslowly added to the liquid nitrogen fixture reservoir until it is full.Liquid nitrogen continues to be added to replace the amount that boilsoff until the liquid nitrogen fixture temperature is stabilized.Stabilization can be confirmed by observing the filter response asdisplayed by the analyzer. The temporary liquid nitrogen fixture coveris removed and laser focus and beam alignment are confirmed by takingadditional test bursts through the quartz window and onto a non-criticalarea of the filter surface. The spiral resonators of the filter are nowready for trimming.

Example 1

This example demonstrates the use of the laser trimming method of theinvention to improve the characteristics of the band-pass region of an8-pole filter with the design shown in FIG. 1, while holding the centerfrequency and the bandwidth of the band-pass region of the filteressentially constant.

The 8-pole HTS filter is produced using double-sided Tl₂Ba₂CaCu₂O₈ filmson a LaAlO₃ substrate and prepared as follows. A clean, polished singlecrystal LaAlO₃ substrate, 75 mm×35 mm×0.5 mm, was obtained from MTICorporation, Richmond, Calif. Off-axis magnetron sputtering of aBa:Ca:Cu oxide target with a stoichiometry of 2:1:2 is used to deposit,at room temperature (about 20° C.), an amorphous precursor Ba:Ca:Cuoxide film onto both sides of the substrate. This amorphous Ba:Ca:Cuoxide film is about 550 nm thick and had a stoichiometry of about 2:1:2.The precursor film is then thallinated by annealing it in air for about10 minutes at 850° C. in the presence of a powder mixture ofTl₂Ba₂Ca₂Cu₃O₁₀ and Tl₂O₃. When this powder mixture is heated, Tl₂Oevolves from the powder mixture, diffuses to the precursor film andreacts with it to form the Tl₂Ba₂CaCu₂O phase.

The Tl₂Ba₂CaCu₂O₈ film surface is then cleaned using an argon ion beam.A gold film is evaporated onto and completely covered the unpatternedTl₂Ba₂CaCu₂O₈ film on the back side of the substrate. The sample is thencoated with photoresist on both sides and baked. The filter design maskwith three filters of the design shown in FIG. 1 is prepared. The HTSlines of each resonator are 300 μm with a gap of 50 μm between the HTSlines. The drawing in FIG. 1 is to scale. The filter design mask is thenplaced on the photoresist covering the Tl₂Ba₂CaCu₂O₈ film on the frontside of the substrate and exposed to ultraviolet light. The resist isthen developed and the portion of the Tl₂Ba₂CaCu₂O₈ film exposed whenthe resist is developed is etched away by argon beam etching. Theremaining photoresist layer is then removed by oxygen plasma. A dicingsaw is then used to section the individual filters. One of these filtersis used in this example.

The filter is then mounted and preparations for trimming are made asdescribed above.

S₁₁ and S₂₁ are measured for the filter before laser trimming and theresults are shown in FIG. 3.

The spiral resonators of the filter underwent the following lasertrimming while monitoring S₁₁ and S₂₁ as provided by the analyzer. Thegoal is to improve the characteristics of the band-pass region whileholding the center frequency and the bandwidth of the band-pass regionof the filter essentially constant. The process used is an iterative oneand essentially the same for each of the spiral resonators in turn.Trimming is begun at the outer end of the spiral of the first spiralresonator. This raised the resonance frequency of the spiral resonator.Trimming at the outer end is continued as long as filter performance asmeasured by S₁₁ and S₂₁ continues to improve. If initial or continuedtrimming at the outer end of the spiral makes performance worse for thisor any of the other spiral resonators, trimming there is stopped andtrimming is begun at an inner corner of the spiral where the currentdensity is sufficiently high so that trimming would result in a decreaseof the resonance frequency. Trimming is continued at this inner corneras long as performance improves. This process is repeated with each ofthe resonators in turn until all 8 spiral resonators had been trimmed.The process of trimming all 8 spiral resonators is repeated 4 moretimes. The number of iterations is dependent upon the filter performanceachieved in comparison to the filter performance desired.

S₁₁ and S₂₁ are measured for the filter after laser trimming and theresults are shown in FIG. 4. Comparison with the results shown in FIG. 3for these coefficients before trimming show that the center frequencyand the bandwidth of the band-pass region remain essentially unchanged.However the magnitude of S₁₁ in the band-pass region has been lowered,resulting in improved filter performance.

Examples 2-4

These examples are carried out using Sonnet EM software, obtained fromSonnet Software, Inc., Liverpool, N.Y. 13088, to simulate theperformance of a HTS spiral resonator and demonstrate the changes in theresonance frequency of the HTS spiral resonator for various amounts ofablation at the outer end of the spiral. The following model is used.The substrate had a thickness of 0.508 mm and a dielectric constant of24 and had a front side and a back side. The spiral resonator is inintimate contact with the front side of the substrate. A ground plane,which in practice would be a blank, i.e. continuous, HTS film, is on theback side of the substrate. The grounded top cover and side walls of thecircuit are all sufficiently far from the spiral resonator so as to havenegligible effect.

The rectangular spiral resonator shown in FIG. 5 is chosen for thesimulation. The line widths of the spiral resonator are 308 μm with agap of 44 μm between lines. The resonance frequency of the spiralresonator with no material removed is 1.8607 GHz. As shown in FIG. 5,material is removed at the outer end of the resonator to simulate theremoval of HTS material there by laser ablation. The amount of materialremoved is a cut of depth d and length l as shown in FIG. 5. In eachexample, the depth of the material removed is the same, i.e. d=44 μm.The lengths l of the cuts are 44 μm for Example 2, 88 μm for Example 3and 132 μm for Example 4. The resonance frequency is next determined forthe spiral resonator of each of the examples. The resonance frequenciesare 1.8613 GHz for Example 2, 1.8617 GHz for Example 3 and 1.8621 GHzfor Example 4. The resonance curves and frequencies are shown in FIG. 6.The increases in resonance frequency from the untrimmed resonancefrequency are summarized in Table I.

TABLE I Increase in Trimming Size Resonance Example (μm) Frequency (MHz)2 44 × 44 0.6 3 44 × 88 1.0 4  44 × 132 1.4

These examples demonstrate the increase in the resonance frequency of aspiral resonator when material is ablated from the outer end of thespiral. The resonance frequency increased more as more material isremoved.

Examples 5-7

These examples are carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 2-4. Asfor the resonator of Examples 2-4, the resonance frequency of the spiralresonator with no material removed is 1.8607 GHz.

As shown in FIG. 7A, for Examples 5-7 material is removed at the innerend 9 of the resonator to simulate the removal of HTS material there bylaser ablation. The location of removal is shown in detail in FIG. 7Bwhere the amount of material removed is shown to be a cut of depth d andlength l. In each example, the depth of the material removed is thesame, i.e. d=44 μm. The lengths l of the cuts are 44 μm for Example 5,88 μm for Example 6 and 132 μm for Example 7. The resonance frequency isdetermined for the spiral resonator of each of the examples. Theresonance frequencies are 1.8605 GHz for Example 5, 1.8603 GHz forExample 6 and 1.8600 GHz for Example 7. The resonance curves andfrequencies are shown in FIG. 8. The decreases in resonance frequencyfrom the untrimmed resonance frequency are summarized in Table II.

TABLE II Decrease in Trimming Size Resonance Example (μm) Frequency(MHz) 5 44 × 44 0.2 6 44 × 88 0.4 7  44 × 132 0.7

These examples demonstrate the decrease in the resonance frequency of aspiral resonator when material is ablated from the inner end of thespiral. The resonance frequency decreased more as more material isremoved. This method of tuning the resonance frequency is subject to theproviso that the depth d of the area to be trimmed at the inner end ofthe spiral of the resonator is small compared to the wavelength λ of thepropagating electromagnetic wave, i.e. that the depth d is less thanabout λ/50. If extensive trimming is carried out at the inner end of thespiral, i.e. such that the depth d is greater than about λ/50, theresonance frequency will increase with increased trimming.

Examples 8-16

These examples are carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 2-4. Asfor the resonator of Examples 2-4, the resonance frequency of the spiralresonator with no material removed is 1.8607 GHz.

As shown in FIG. 9A, for Examples 8-16 material is removed near a cornerat the inner edge of the HTS spiral line of the resonator to simulatethe removal of HTS material there by laser ablation. The three locationsat which material is removed are shown as A, B and C on FIG. 9A.Examples 8-10 are carried out at location A. Examples 11-13 are carriedout at location B. Examples 14-16 are carried out at location C. Thematerial removed is shown in detail in FIG. 9B where the amount ofmaterial removed is shown to be a cut of width d and length l. In eachexample, the width of the material removed is the same, i.e. d=44 μm.The lengths l of the cuts are 44 μm for Examples 8, 11 and 14, 88 μm forExamples 9, 12 and 15 and 132 μm for Examples 10. The resonancefrequency is determined for the spiral resonator of each of theexamples. The resonance curves are similar in shape to those shown inFIGS. 6 and 8. The resonance frequencies and the decreases in resonancefrequency from the untrimmed resonance frequency are summarized in TableIII.

TABLE III Decrease in Resonance Trimming Size Resonance FrequencyExample (μm) Frequency (MHz) (GHz) 8 44 × 44 0.4 1.8603 9 44 × 88 1.21.8595 10  44 × 132 2.3 1.8584 11 44 × 44 0.1 1.8606 12 44 × 88 0.81.8599 13  44 × 132 1.6 1.8591 14 44 × 44 0.0 1.8607 15 44 × 88 0.51.8602 16  44 × 132 1.2 1.8595

These examples demonstrate the decrease in the resonance frequency of aspiral resonator when material is ablated from an interior location onthe inner edge of the spiral where there are higher current densities.Ablation is most effective in reducing the resonance frequency forlocation A, which is closest to the corner and where a higher currentdensity is expected. Location B is farther from the corner with asmaller current density and showed smaller decreases in resonancefrequency for the same degree of ablation. Location C is farthest fromthe corner with the smallest current density and showed the smallestdecreases in resonance frequency for the same degree of ablation. Thedecrease in resonance frequency for Example 14 is less than 0.1 MHz. Ateach location, the resonance frequency decreased more as more materialis removed.

Examples 17-20

These examples are carried out using Sonnet EM software, obtained fromSonnet Software, Inc., Liverpool, N.Y. 13088, to simulate theperformance of a HTS spiral resonator and demonstrate the changes in theresonance frequency of the HTS spiral resonator for various amounts ofablation at the outer end of the spiral. The following model is used.The substrate had a thickness of 0.508 mm and a dielectric constant of24 and had a front side and a back side. The spiral resonator is inintimate contact with the front side of the substrate. A ground plane,which in practice would be a blank, i.e. continuous, HTS film, is on theback side of the substrate. The circuit box size is 11.264 mm×7.48mm×5.0 mm. A rectangular spiral resonator shown in FIG. 10 is chosen forthe simulation. The line widths of the spiral resonator are 308 μm witha gap of 44 μm between lines. The resonance frequency of the spiralresonator with no material removed is 1.88671 GHz. Various locations onthe spiral resonator are indicated by the letters a-n on FIG. 10.

FIG. 11 is an enlarged view of location a, the outer end of the HTSspiral line shown in FIG. 10. As shown in FIG. 11, for Examples 17-20,material is removed to simulate the removal of HTS material there bylaser ablation. The amount of material removed in Examples 17, 18 and 19is a cut 44 μm wide and 88 μm into the end of the HTS line at locationsa₁, a₂ and a₃, respectively, as shown in FIG. 11. The amount of materialremoved in Example 20 is a cut 44 μm into the end of the HTS line acrossthe whole width of the HTS line and indicated by the cross-hatched areaa₄ of FIG. 11. The resonance frequency is determined for the spiralresonator of each of the Examples. The resonance curves are similar inshape to those shown in FIGS. 6 and 8. The resonance frequencies and theincreases in resonance frequency from the untrimmed resonance frequencyare summarized in Table IV.

TABLE IV Increase in Resonance Resonance Frequency Example Frequency(MHz) (GHz) 17 1.83 1.88854 18 1.01 1.88772 19 0.21 1.88692 20 4.381.89109

These examples demonstrate the increase in the resonance frequency of aspiral resonator when material is ablated from the outer end of thespiral. The magnitude of the increase depends upon the location of theablation and the amount of material removed.

Examples 21-24

These examples are carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 17-20.As for the resonator of Examples 17-20, the resonance frequency of thespiral resonator with no material removed is 1.88671 GHz.

FIG. 12 is an enlarged view of location n, the inner end of the HTSspiral line shown in FIG. 10. As shown in FIG. 12, for Examples 21-24,material is removed to simulate the removal of HTS material there bylaser ablation. The amount of material removed in Examples 21, 22 and 23corresponds to a cut 44 μm wide and 88 μm into the end of the HTS lineat locations n₁, n₂ and n₃, respectively, as shown in FIG. 12. Theamount of material removed in Example 24 corresponds to a cut 44 μm intothe end of the HTS line across the whole width of the HTS line andindicated by the cross-hatched area n₄ of FIG. 12. The resonancefrequency is determined for the spiral resonator of each of theexamples. The resonance curves are similar in shape to those shown inFIGS. 6 and 8. The resonance frequencies and the decreases in resonancefrequency from the untrimmed resonance frequency are summarized in TableV.

TABLE V Decrease in Resonance Resonance Frequency Example Frequency(MHz) (GHz) 21 0.55 1.88616 22 0.53 1.88618 23 1.38 1.88533 24 1.601.88511

These examples demonstrate the decrease in the resonance frequency of aspiral resonator when material is ablated from the inner end of thespiral. The magnitude of the decrease depends upon the location of theablation and the amount of material removed.

Example 25

This example is carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 17-20.As for the resonator of Examples 17-20, the resonance frequency of thespiral resonator with no material removed is 1.88671 GHz.

Material is removed from the inner edge of the HTS spiral line at theinterior locations b-k shown in FIG. 10 to simulate the removal of HTSmaterial at these locations by laser ablation. Each of these locationsis near a corner of the HTS spiral resonator. The amount of materialremoved at each location is a cut 44 μm wide and 88 μm deep. The cutbegan 99 μm away from the nearest corner to the location indicated andis 44 μm wide. It extended 88 μm into the spiral line. One such cut isshown at g in FIG. 13. The resonance frequency is determined for thespiral resonator with the material removed at each of the similarlocations near the corners b-k shown in FIG. 10. The resonance curvesare similar in shape to those shown in FIGS. 6 and 8. The shift in theresonance frequency observed as a result of trimming only at thelocation indicated is plotted in FIG. 14 for each of the locations b-k.Current density data is obtained by simulating a 1 volt source appliedto the spiral resonator with no material removed. Peak current densityis readily obtained from simulation data, and is used herein as ameasure of current density. An alternative, however, would be to use theaverage current density at the area being trimmed as a measure ofcurrent density rather than peak current density. The current densitiesobtained using the software are linear current densities. The peakcurrent density, with no material removed, at each of the locations b-kis also plotted in FIG. 14.

For location b, there is a small current density and a small positivefrequency shift, i.e. a small increase in resonance frequency. For allother locations the current density is relatively higher and there is anegative frequency shift, i.e. a decrease in resonance frequency.Location g has the highest current density and the largest decrease inresonance frequency. This example demonstrates that the spiral resonatorresonance frequency can be adjusted by trimming at various interiorlocations and that the amount of adjustment, for a given amount ofmaterial remove, depends on the location of the trimming, i.e. on thecurrent density at that location.

Example 26

This example is carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 17-20.As for the resonator of Examples 17-20, the resonance frequency of thespiral resonator with no material removed is 1.88671 GHz.

Material is removed from the inner edge of the HTS spiral line atinterior locations that are midway between the corners b-k shown in FIG.10 to simulate the removal of HTS material at these locations by laserablation. The inner edge midpoint between end a and corner b isdesignated as ab, the inner edge midpoint between corner b and corner cis designated by bc, etc. The amount of material removed at each inneredge midpoint location is a cut 44 μm wide extending 88 μm into thespiral line. One such cut for the inner edge midpoint between thecorners e and f, i.e. location ef, is shown in FIG. 13. The resonancefrequency is determined for the spiral resonator with the materialremoved at each of the inner edge midpoint locations ab-jk. Theresonance curves are similar in shape to those shown in FIGS. 6 and 8.The shift in the resonance frequency observed as a result of trimmingonly at the location indicated is plotted in FIG. 15 for each of theinner edge midpoint locations ab-jk. Current density data is obtained asdescribed in Example 25 and the peak current density, with no materialremoved, at each of the locations ab-jk is also plotted in FIG. 15.

For locations ab and bc, there are small current densities and smallpositive frequency shifts, i.e. small increases in resonance frequency.For all other locations the current density is relatively higher, andthere is a negative frequency shift, i.e. a decrease in resonancefrequency. The locations with the higher current densities have largerdecreases in resonance frequency. This example demonstrates that thespiral resonator resonance frequency can be adjusted by trimming atvarious interior locations and that the amount of adjustment, for agiven amount of material remove, depends on the location of thetrimming, i.e. on the current density at that location.

Example 27

This example is carried out using the same Sonnet EM software and thesame rectangular spiral resonator and substrate used in Examples 17-20.As for the resonator of Examples 17-20, the resonance frequency of thespiral resonator with no material removed is 1.88671 GHz.

Material is removed from the outer edge of the HTS spiral line atinterior locations that are midway between the corners b-k shown in FIG.10 to simulate the removal of HTS material at these locations byablation. The outer edge midpoint between end a and corner b isdesignated as ab′, the outer edge midpoint between corner b and corner cis designated by bc′, etc. The amount of material removed at each outeredge midpoint location is a cut 44 μm wide extending 88 μm into thespiral line. One such cut for the outer edge midpoint between the end aand the corner b, i.e. location ab′, is shown in FIG. 13. The resonancefrequency is determined for the spiral resonator with the materialremoved at each of the outer edge midpoint locations ab′-jk′. Theresonance curves are similar in shape to those shown in FIGS. 6 and 8.The shift in the resonance frequency observed as a result of trimmingonly at the location indicated is plotted in FIG. 16 for each of theouter edge midpoint locations ab′-jk′. Current density data is obtainedas described in Example 25 and the peak current density, with nomaterial removed, at each of the locations ab′-jk′ is also plotted inFIG. 16.

The dependence of the peak current density with outer edge midpointlocations along the spiral line varies considerably. The current densityhas a moderate magnitude at ab′, toward the outer end of the spiralline, increases through a maximum at location de′, decreases to aminimum at gh′ and then increases along the spiral line toward the innerend. The frequency shift changes correspondingly. For locations alongthe outer portion of the spiral line the frequency shifts are negative,i.e. there are decreases in resonance frequency. The frequency shift issmall and positive for gh′ and then becomes negative for locationscloser to the inner end of the spiral line. This example demonstratesthat the spiral resonator resonance frequency can be adjusted bytrimming at various interior locations, and that the amount ofadjustment, for a given amount of material remove, depends on thelocation of the trimming, i.e. on the current density at that location.

Comparison with Example 26 shows that trimming by the same amount at agiven location along the spiral line can result in quite differentresults depending on whether the tuning is along the inner edge of theline or the outer edge. Trimming at inner edge locations gh and hi inExample 26 resulted in large decreases in the resonance frequency.Trimming at outer edge locations gh′ and hi′ in Example 27 resulted insmall increases in the resonance frequency. In contrast, trimming atinner edge de and outer edge de′ resulted in about the same decrease inresonance frequency.

To demonstrate the importance of the current density in determining theeffect on the resonance frequency of a given amount of trimming atinterior locations along the spiral line, FIG. 17 shows a plot of thefrequency shifts observed at the various locations in Examples 25, 26and 27 versus the peak current densities at those locations. Theresulting shifts from trimming at interior points along the spiral lineis approximately linearly dependent on the peak current density at thelocation of the trim as shown by the line drawn on FIG. 17. It isbelieved that if the frequency shift had been plotted versus averagecurrent density the linear fit would be even better.

Example 28

This example demonstrates the use of the laser trimming method of theinvention to lower the center frequency of the band-pass region of an8-pole filter with the design shown in FIG. 1, while holding thebandwidth of the band-pass region of the filter essentially constant.

The 8-pole HTS filter is produced using essentially the same procedureas used in Example 1.

The filter is mounted and preparations for trimming are made asdescribed above.

S₁₁ and S₂₁ are measured for the filter before laser trimming and theresults are shown in FIG. 18.

The spiral resonators of the filter underwent laser trimming in a mannersimilar to that described in Example 1. However, since the goal in thisexample is to lower the center frequency of the band-pass while holdingthe bandwidth of the band-pass region of the filter essentiallyconstant, trimming is begun at an inner corner of the spiral of thefirst spiral resonator where the current density is sufficiently high sothat trimming would result in a decrease of the resonance frequency.Trimming continued at this inner corner as long as performance improved.Trimming is then shifted to the outer end of the spiral to determine iftrimming there improved performance. Each of the 8 spiral resonators istrimmed in a similar manner. The process of trimming all 8 spiralresonators is repeated 6 more times. Larger frequency shifts areaccomplished with the first few iterations, and finer tuning andimprovements in S₁₁ and S₂₁ are accomplished with the later iterations.

S₁₁ and S₂₁ are measured for the filter after laser trimming, and theresults are shown in FIG. 19. Comparison with the results shown in FIG.18 for these coefficients before trimming show that the center frequencyis shifted downward about 6 MHz. The magnitude of S₁₁ in the band-passregion has also been lowered resulting in improved filter performance.The bandwidth of the band-pass region remains essentially unchanged.

Example 29

This example demonstrates the use of the laser trimming method of theinvention to raise the center frequency of the band-pass region of an8-pole filter with the design shown in FIG. 1, while holding thebandwidth of the band-pass region of the filter essentially constant.

The 8-pole HTS filter is produced using essentially the same procedureas used in Example 1.

The filter is mounted and preparations for trimming are made asdescribed above.

S₁₁ and S₂₁ are measured for the filter before laser trimming and theresults are shown in FIG. 20.

The spiral resonators of the filter underwent laser trimming in a manneranalogous to that described in Example 1. Since the goal in this Exampleis to raise the center frequency of the band-pass while holding thebandwidth of the band-pass region of the filter essentially constant,trimming is begun at the outer end of the spiral of the first spiralresonator in order to raise the resonance frequency of that resonator.Trimming continued at this outer end as long as performance improved.Trimming then shifted to an inner corner of the spiral of the firstspiral resonator, where the current density is sufficiently high so thattrimming would result in a decrease of the resonance frequency, todetermine if trimming there improved performance. Each of the 8 spiralresonators is trimmed in a similar manner. The process of trimming all 8spiral resonators is repeated 6 more times. Larger frequency shifts areaccomplished with the first few iterations, and finer tuning andimprovements in S₁₁ and S₂₁ are accomplished with the later iterations.

S₁₁ and S₂₁ are measured for the filter after laser trimming, and theresults are shown in FIG. 21. Comparison with the results shown in FIG.20 for these coefficients before trimming shows that the centerfrequency is shifted upward about 7 MHz. The magnitude of S₁₁ in theband-pass region has been lowered resulting in improved performance. Thebandwidth of the band-pass region remains essentially unchanged.

Example 30

This example demonstrates the use of the laser trimming method of theinvention to improve the characteristics of the band-pass region of an8-pole filter with the design shown in FIG. 1, while holding the centerfrequency and the bandwidth of the band-pass region of the filteressentially constant.

The 8-pole HTS filter is produced using essentially the same procedureas used in Example 1.

The filter is then mounted and preparations for trimming are made asdescribed above.

S₁₁ and S₂₁ are measured for the filter before laser trimming and theresults are shown in FIG. 22.

Since the goal in this Example is the same as that of Example 1, i.e. toimprove the characteristics of the band-pass region of an 8-pole filterwith the design shown in FIG. 1, while holding the center frequency andthe bandwidth of the band-pass region of the filter essentiallyconstant, the spiral resonators of the filter underwent laser trimmingessentially as described in Example 1.

S₁₁ and S₂₁ are measured for the filter after laser trimming and theresults are shown in FIG. 23. Comparison with the results shown in FIG.22 for these coefficients before trimming show that the center frequencyand the bandwidth of the band-pass region remain essentially unchanged.However, the magnitude of S₁₁ in the band-pass region has been lowered,and the magnitude of S₂₁ in the band-pass region has been raisedresulting in improved filter performance.

Where an apparatus or method of this invention is stated or described ascomprising, including, containing, having, being composed of or beingconstituted by certain components or steps, it is to be understood,unless the statement or description explicitly provides to the contrary,that one or more components or steps other than those explicitly statedor described may be present in the apparatus or method. In analternative embodiment, however, the apparatus or method of thisinvention may be stated or described as consisting essentially ofcertain components or steps, in which embodiment components or stepsthat would materially alter the principle of operation or thedistinguishing characteristics of the apparatus or method would not bepresent therein. In a further alternative embodiment, the apparatus ormethod of this invention may be stated or described as consisting ofcertain components or steps, in which embodiment components or stepsother than those as stated would not be present therein.

Where the indefinite article “a” or “an” is used with respect to astatement or description of the presence of a component in an apparatus,or a step in a method, of this invention, it is to be understood, unlessthe statement or description explicitly provides to the contrary, thatthe use of such indefinite article does not limit the presence of thecomponent in the apparatus, or of the step in the method, to one innumber.

1-18. (canceled)
 19. A process for forming a high temperaturesuperconductor circuit element, comprising: (a) forming a film of a hightemperature superconductor material on a substrate; and (b) ablatingselected regions of the high temperature superconductor film with alaser beam while protecting from ablation other regions of the hightemperature superconductor film that form a pattern of the circuitelement.
 20. The process of claim 19, wherein the high temperaturesuperconductor circuit element is a high temperature superconductorfilter.
 21. The process of claim 20, wherein the high temperaturesuperconductor filter is comprised of at least two high temperaturesuperconductor spiral resonators.
 22. The process of claim 19, whereinthe high temperature superconductor circuit element is a hightemperature superconductor coil.
 23. The process of claim 22, whereinthe high temperature superconductor coil is a high temperaturesuperconductor planar coil.
 24. A method for tuning the resonancefrequency of a high temperature superconductor planar coil, comprisingablating portions of the high temperature superconductor of the hightemperature superconductor planar coil with a laser beam.
 25. The methodof claim 24, wherein the resonance frequency is increased by ablatingthe high temperature superconductor at the outer end of the hightemperature superconductor planar coil.
 26. The method of claim 24,wherein the resonance frequency is increased by ablating the hightemperature superconductor at the inner end of the high temperaturesuperconductor planar coil.
 27. The method of claim 24, wherein theresonance frequency is tuned by ablating the high temperaturesuperconductor in at least one interior location along the hightemperature superconductor planar coil.
 28. The method of claim 27,wherein the amount of current density at the interior location of thehigh temperature superconductor planar coil is sufficiently low toresult in an increase in the resonance frequency as a result of laserablation.
 29. The method of claim 27, wherein the amount of currentdensity at the interior location of the high temperature superconductorplanar coil is sufficiently high to result in a decrease in theresonance frequency as a result of laser ablation.
 30. The method ofclaim 24, wherein the resonance frequency is increased by ablating thehigh temperature superconductor at one or more of the followinglocations: (a) at the outer end of the high temperature superconductorplanar coil; (b) at the inner end of the high temperature superconductorplanar coil; and (c) in at least one interior location of the hightemperature superconductor planar coil at which the current density issufficiently low to result in an increase in the resonance frequency asa result of laser ablation.
 31. The method of claim 24, wherein theresonance frequency is decreased by ablating the high temperaturesuperconductor in at least one interior location of the high temperaturesuperconductor planar coil at which the current density is sufficientlyhigh to result in a decrease in the resonance frequency as a result oflaser ablation. 32-37. (canceled)